STATUS OF 12 C + a REACTIONS FROM AN R-MATRIX VIEWPOINT RICHARD DEBOER TRENTO, ITALY 2013

Transcription

1 STATUS OF 12 C + a REACTIONS FROM AN R-MATRIX VIEWPOINT RICHARD DEBOER TRENTO, ITALY 2013

2 OUTLINE What data is considered? The R-matrix Fit Successes and remaining problems Uncertainty analysis Monte Carlo

3 SOME BACKGROUND 15 N(p,g) 16 O 15 N(p,p 0 ) 15 N 15 N(p,a) 12 C 15 N(p,a 1 ) 12 C 12 C(a,g) 16 O 12 C(a,a 0 ) 12 C 12 C(a,p) 15 N 12 C(a,a 1 ) 12 C???

4 R-matrix theory: reaction framework for low energy nuclear reactions Based on the algorithms developed for AZURE FORTRAN by R.E. Azuma Written in C++, Graphical Interface created with Qt Utilizes currently maintained pubic libraries MINUIT2 GNU Scientific Library Open Source soon Multiple entrance/exit channels Particle, particle Particle, gamma Beta delayed particle emission Full external capture calculation with E1, E2, and M1 as well as contributions to the gamma widths of resonances AZURE2

5 SCHÜRMANN ET AL. (2012) Global analysis of 12 C(a,g) 16, 16 N(ba) 12 C, and 12 C(a,a) 12 C phase shifts Systematic Uncertainties considered Monte Carlo uncertainty analysis S(300 kev) = (stat) +8-2 (syst) Independent analysis Consider broader set of data Extend uncertainty analysis to entire cross section curve and to reaction rate over a broad temperature range

6 SYSTEMATIC UNCERTAINTY Schürmann et al. (2012)

7 HIGHER ENERGY DATA

8 HIGH ENERGY DATA 1-1 -

9 LOW ENERGY DATA Total data points to date: 12600

10 FULL ANALYSIS REGION Tischhauser et al. (2009) Azuma et al. (1994) Schürmann et al. (2005)

11 WHAT MAKES 12 C(a,g) 16 O SO TOUGH FOR R-MATRIX? Subthreshold states (E x = 7.12 and 6.92 MeV) Broad resonances with strong interferences Direct Capture E1 and E2 components

12 12 C(a,g 0 ) 16 O 12 LOW ENERGY MEASUREMENTS Brochard et al. (1973) Dyer and Barns (1974) Kettner et al. (1982) Redder et al. (1987) Kremer et al. (1988) Ouellet et al. (1996) Roters et al. (1999) Gialanella et al. (2001) Kunz et al. (2001) Fey Thesis (2004) Assuncao et al. (2006) Makii et al. (2009) Schürmann et al. (2011)

13 GROUND STATE ANGULAR DISTRIBUTIONS

14 MORE GROUND STATE ANGULAR DISTRIBUTIONS

15 E2 INTERFERENCE

16 E1 INTERFERENCE: TWO SOLUTIONS Michael Fey Thesis (2004) systematic study of interferences c 2 /n = 2.5 c 2 /n = 9.0 c 2 /n = 8.6 Current analysis n = 146 c 2 /n = 9.6

17 16 N(ba) 12 C a) Azuma et al. (1994) b) Tang et al. (2010) Also seen recently in Schürmann et al. (2012) Data sets have some dissagreements

18 CASCADE TRANSITIONS Redder et al. (1987) Kunz (priv. comm.) Schürmann et al. (2011) Matei et al. (2006) Kettner et al. (1982)

19 CASCADE TRANSITION ISSUES For previous fit, ANC of 6.05 MeV state was about 1600 fm -1/2 Fairouz Hammache, private communication

20 12 C(a,a 0 ) 12 C TISCHHAUSER ET AL. (2002) & (2009)

21 FIT SUMMARY Generally good fit for all data Issues Beta delayed particle emission data Cascade transition data 6.13 and 6.05 MeV transitions The data constrain the interferences, transfer measurements constrain the low energy cross section and uncertainty Background poles for 12 C(a,g 0 ) 16 O may not be necessary

22 ASYMPTOTIC NORMALIZATION COEFFICIENTS Contribution of the subthreshold states is determined by ANCs and g widths ANCs can be constrained by (see Mukhamedzhanov and Tribble (1998) ) scattering data -- BGP ( ) beta delayed emission -- BGP ( ) 12 C(a,g) 16 O and 6.92 transitions need data transfer reactions ( )

23 THE SUBTHRESHOLD STATES: ANCs Ground State F. Hammache, private communication

24 SUBTHRESHOLD STATES: g WIDTHS

25 MONTE CARLO UNCERTAINTY ANALYSIS Multiparameter fit function uncertainties tough to extract parameter correlations reaction rate Monte Carlo method assume data point uncertainties are Gaussian assume systematic uncertainties are Gaussian or Linear Best fit is an accurate description of the true cross section Create new data sets from random variations and do analysis again

26 PROBABILITY DENSITY FUNCTION Only 1000 throws

27 RECENT ESTIMATES OF S(300 KEV) Woosley, Heger, and Weaver (2002) want DS(300 kev) < 10%

28 PRELIMINARY UNCERTAINTY S(300 KEV) = 160 (10% + MODEL) KEV B

29 FUTURE Model uncertainties must be estimated radius parameter background poles What is going on with the a radius parameter? Higher angular momentum terms necessary? Narrow resonance contributions to the rate

30 CONCLUSIONS ANCs dominate the low energy uncertainty Including higher energy data decreases the dependence of the R-matrix fit on background poles 12 C(a,g) 16 O cross section may be approaching the 10% level of uncertainty Cascade transitions are worth measuring don t contribute much to the total but are very helpful for the R-matrix analysis of the total cross section data

31 COLLABORATORS J. Görres K. Smith E. Uberseder M. Wiescher THANKS TO R.E. Azuma C. Brune D. Schürmann G. Imbriani F. Strieder and many others